# Integrating Using Arctan

Integrate
1/(x2 +11x +29)

## The Attempt at a Solution

I'm doing something wrong, but can't figure out what...

Complete the square so that the denominator equals (x+2)2+25

Then divide by 25: ((x+2)2)/25 + 1

Move that 25 into the squared part: ((x+2)/5)2+1

Substitute the squared part for u.

Find du/dx = 1/5, and therefore 5du=dx

Now we have 5*(integral sign) du / (u2+1)

This gives 5arctan(u)+C --> substitute u back for what you had before.

But the answer is 1/5arctan(u). Where did I go wrong?

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## Answers and Replies

When you "divide by 25", where does that 25 go?

Oops, I was focusing so much on the denominator, I forgot about the numerator. This is what happens when yiou do math late at night, haha.

Thanks!

Dick
Science Advisor
Homework Helper
You can't just divide by something and expect the answer to be unchanged. Once you have 1/((x+5)^2+25) why not just substitute (x+5)=5*u?

djeitnstine
Gold Member
how about x+2 = 5tanu to make life easier